No-fives subgroup temperaments: Difference between revisions
→Temperaments with a 2.3.13 gene: move full data for tridecapyth here |
|||
| Line 1,043: | Line 1,043: | ||
== Temperaments with a 2.3.13 gene == | == Temperaments with a 2.3.13 gene == | ||
=== Threedic === | === Threedic === | ||
[[Subgroup]]: 2.3.13 | [[Subgroup]]: 2.3.13 | ||
| Line 1,089: | Line 1,080: | ||
[[Badness]] (Sintel): 0.200 | [[Badness]] (Sintel): 0.200 | ||
=== Tridecapyth === | |||
Tridecapyth sets a stack of ten [[9/8]]'s equal to [[13/4]]. It can be seen as a way of giving a mapping of prime 13 to any temperament with an extremely accurate tuning of its fifth (like the [[53edo]] tuning of [[schismic]]). Interestingly, the mapping is ''so'' accurate that more optimized tunings of schismic that use a flatter fifth are not accurate enough to preserve the mapping; for 118edo we get the 118f [[val]] that takes the second-best, flat mapping of prime 13, and the same is true for [[171edo]] where we get the 171f val. However, due to its small note count, [[41edo]] technically uses this mapping too, so that [[94edo]], the val sum of 41 and 53, also uses this mapping, suggesting it is of interest to flatter tunings of [[garibaldi]] with fifths tending close to pure; this corresponds to the extension of garibaldi called [[cassandra]]. If we add this mapping to 5-limit schismic instead we get [[tridecaschismic]]. | |||
[[Subgroup]]: 2.3.13 | |||
{{mapping|legend=2| 1 0 -28 | 0 1 20 }} | |||
: mapping generators: ~2, ~3 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.9778{{c}}, ~3/2 = 702.0170{{c}} | |||
: [[error map]]: {{val| -0.022 +0.040 -0.011 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0283{{c}} | |||
: error map: {{val| 0.000 +0.070 -0.019 }} | |||
{{Optimal ET sequence|legend=1| 12, 29f, 41, 53, 94, 147, 494, 641, 788, 2217, 3005 }} | |||
[[Badness]] (Sintel): 0.211 | |||
=== Superflat === | === Superflat === | ||